Vol. 56, No. 1, 1975

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
Central embeddings in semi-simple rings

Shimshon A. Amitsur

Vol. 56 (1975), No. 1, 1–6
Abstract

A ring S is a central extension of a subring R if S = RC and C is the centralizer of R in S, i.e., C = {s S;sr = rs} for every r R. We shall also say that R is centrally embedded in

S.

We have shown that if a ring R is centrally embedded in a simple artinian ring then R is a prime Öre ring and its quotient ring Q is the minimal central extension of R which is a simple artinian ring; furthermore, the centralizer of R can be characterized. In the present note we extend these results and show that rings which can be centrally embedded in semi-simple artinian rings are semi-prime Öre rings with a finite number of minimal primes and their rings of quotients are the minimal central extension of this type.

Mathematical Subject Classification
Primary: 16A08
Milestones
Received: 28 December 1973
Published: 1 January 1975
Authors
Shimshon A. Amitsur